Tracing patterns and shapes in remittance and migration networks via persistent homology

Ignacio, Paul Samuel; Darcy, Isabel K.

doi:10.1140/epjds/s13688-018-0179-z

Cited by 23 publications

(24 citation statements)

References 35 publications

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“…Many biological applications to proteins and DNA rely on the ability of PH to illuminate features at multiple scales, as multiscale structures and compositions of these molecules are extremely important to their function. PH has also been applied to larger-scale biological systems, including leaf-venation patterns [40], aggregation models [41], human migration [42], networks of blood vessels [43], and the effects of psychoactive substances on brain activity [44]. The recent review article [45] includes an extensive discussion of applications of PH to networks.…”

Section: Introductionmentioning

confidence: 99%

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Feng

Porter

2020

Phys. Rev. Research

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Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks-including both synthetic and natural ones-using topological methods that we developed recently for analyzing spatial systems. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs that were spun by spiders under the influence of various psychotropic substances.

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Section: Introductionmentioning

confidence: 99%

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Feng

Porter

2020

Phys. Rev. Research

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“…Also, topological detection in network models might provide insights in both global structure and local node interactions, either in natural or artificial neural networks and in lattice percolation procedures. Further, unknown patterns assessed through topological weapons could be useful in understanding economic and sociologic trends of migratory fluxes (Ignacio and Darcy, 2019). Our technique of hole detection might also allow to assess the discrete dynamic changes and multi-dynamic clustering occurring at the macroscales of galaxies, cosmic bodies and Megaparsec web-like cosmic matter distribution, describing the topological invariants of their subtending networks (Pranav et al, 2016) and, possibly, providing better insights in dark matter and vacuum energy.…”

Section: Discussionmentioning

confidence: 99%

Topological Assessment of Unidentified Moving Objects

Tozzi¹,

Peters²

2019

Preprint

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Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects' sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks' and cosmic bodies' analysis.

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“…In practice, in an oriented k-simplex, each node is made to point only to nodes with a higher assigned number. Oriented simplicial complexes arise in practice from directed synapses between neurons [169] as well as directed migration flow [101]. Finally, in hypergraphs, one may represent directionality with hyperarcs, the term for a directed hyperedge.…”

Section: Directedmentioning

confidence: 99%

The Why, How, and When of Representations for Complex Systems

Torres¹,

Blevins²,

Bassett³

et al. 2021

SIAM Rev.

164

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Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics. The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are seldom revisited, and the compartmentalization of representation and analysis ideas within a domain due to inconsistency in complex systems language. In this work we propose basic, domain-agnostic language in order to advance toward a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system under study and data collected, then moving through different mathematical frameworks for encoding the observed data (i.e., graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each framework. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of an interaction among a set of units in a system may affect the possibility of the existence of another relation. We discuss how dependencies may arise and how they may alter the interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and the choice of mathematical representation influence the results. We hope this work can serve as an opportunity for reflection for experienced complex systems scientists, as well as an introductory resource for new researchers.

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Tracing patterns and shapes in remittance and migration networks via persistent homology

Cited by 23 publications

References 35 publications

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Topological Assessment of Unidentified Moving Objects

The Why, How, and When of Representations for Complex Systems

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